LMFDB - Embedded newform 275.3.d.b.274.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(274,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.274"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 50x^{14} + 939x^{12} + 8450x^{10} + 39245x^{8} + 93316x^{6} + 104420x^{4} + 45264x^{2} + 6400 $ x^16 + 50x^14 + 939x^12 + 8450x^10 + 39245x^8 + 93316x^6 + 104420x^4 + 45264*x^2 + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.14
Root			$-1.78271i$ of defining polynomial
Character	$\chi$	$=$	275.274
Dual form			275.3.d.b.274.13

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.78271 q^{2} +5.54645i q^{3} +3.74350 q^{4} +15.4342i q^{6} -4.48239 q^{7} -0.713764 q^{8} -21.7632 q^{9} +(2.46337 + 10.7206i) q^{11} +20.7632i q^{12} +15.7063 q^{13} -12.4732 q^{14} -16.9602 q^{16} +25.4820 q^{17} -60.5607 q^{18} +8.44528i q^{19} -24.8614i q^{21} +(6.85487 + 29.8324i) q^{22} -19.8870i q^{23} -3.95886i q^{24} +43.7063 q^{26} -70.7903i q^{27} -16.7798 q^{28} +21.4524i q^{29} +24.9579 q^{31} -44.3404 q^{32} +(-59.4615 + 13.6630i) q^{33} +70.9092 q^{34} -81.4704 q^{36} +30.4659i q^{37} +23.5008i q^{38} +87.1145i q^{39} +10.5577i q^{41} -69.1821i q^{42} +68.3676 q^{43} +(9.22164 + 40.1327i) q^{44} -55.3397i q^{46} +25.0636i q^{47} -94.0690i q^{48} -28.9082 q^{49} +141.335i q^{51} +58.7967 q^{52} -93.9329i q^{53} -196.989i q^{54} +3.19936 q^{56} -46.8414 q^{57} +59.6960i q^{58} +27.3730 q^{59} -81.1075i q^{61} +69.4507 q^{62} +97.5509 q^{63} -55.5457 q^{64} +(-165.464 + 38.0202i) q^{66} +49.5118i q^{67} +95.3920 q^{68} +110.302 q^{69} +44.0132 q^{71} +15.5338 q^{72} -29.1783 q^{73} +84.7779i q^{74} +31.6149i q^{76} +(-11.0418 - 48.0540i) q^{77} +242.415i q^{78} -51.3920i q^{79} +196.767 q^{81} +29.3792i q^{82} +47.2115 q^{83} -93.0685i q^{84} +190.248 q^{86} -118.985 q^{87} +(-1.75827 - 7.65199i) q^{88} -147.455 q^{89} -70.4019 q^{91} -74.4468i q^{92} +138.428i q^{93} +69.7449i q^{94} -245.932i q^{96} -87.8176i q^{97} -80.4433 q^{98} +(-53.6108 - 233.315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{4} - 64 q^{9} - 2 q^{11} - 36 q^{14} - 28 q^{16} + 136 q^{26} - 84 q^{31} + 284 q^{34} - 168 q^{36} - 138 q^{44} + 100 q^{49} + 332 q^{56} + 320 q^{59} - 576 q^{64} - 630 q^{66} + 32 q^{69}+ \cdots - 736 q^{99}+O(q^{100}) $ 16 * q + 20 * q^4 - 64 * q^9 - 2 * q^11 - 36 * q^14 - 28 * q^16 + 136 * q^26 - 84 * q^31 + 284 * q^34 - 168 * q^36 - 138 * q^44 + 100 * q^49 + 332 * q^56 + 320 * q^59 - 576 * q^64 - 630 * q^66 + 32 * q^69 + 492 * q^71 + 608 * q^81 - 564 * q^86 + 36 * q^89 - 284 * q^91 - 736 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.78271			1.39136			0.695679	−	0.718353i	$-0.255104\pi$
$2$	2.78271			1.39136			0.695679	+	0.718353i	$0.255104\pi$
$3$			5.54645i			1.84882i	0.381402	+	0.924409i	$0.375441\pi$
$3$			5.54645i			1.84882i	−0.381402	+	0.924409i	$0.624559\pi$
$4$	3.74350			0.935875
$5$		0			0
$5$		0			0
$6$			15.4342i			2.57237i
$7$	−4.48239			−0.640341			−0.320170	−	0.947360i	$-0.603740\pi$
$7$	−4.48239			−0.640341			−0.320170	+	0.947360i	$0.603740\pi$
$8$	−0.713764			−0.0892205
$9$	−21.7632			−2.41813
$10$		0			0
$11$	2.46337	+	10.7206i	0.223943	+	0.974602i
$11$	2.46337	+	10.7206i	0.223943	+	0.974602i
$12$			20.7632i			1.73026i
$13$	15.7063			1.20818			0.604090	−	0.796916i	$-0.293537\pi$
$13$	15.7063			1.20818			0.604090	+	0.796916i	$0.293537\pi$
$14$	−12.4732			−0.890943
$15$		0			0
$16$	−16.9602			−1.06001
$17$	25.4820			1.49894			0.749471	−	0.662037i	$-0.230308\pi$
$17$	25.4820			1.49894			0.749471	+	0.662037i	$0.230308\pi$
$18$	−60.5607			−3.36448
$19$			8.44528i			0.444488i	0.974991	+	0.222244i	$0.0713382\pi$
$19$			8.44528i			0.444488i	−0.974991	+	0.222244i	$0.928662\pi$
$20$		0			0
$21$		−	24.8614i		−	1.18387i
$22$	6.85487	+	29.8324i	0.311585	+	1.35602i
$23$		−	19.8870i		−	0.864650i	−0.901718	−	0.432325i	$-0.857693\pi$
$23$		−	19.8870i		−	0.864650i	0.901718	−	0.432325i	$-0.142307\pi$
$24$		−	3.95886i		−	0.164952i
$25$		0			0
$26$	43.7063			1.68101
$27$		−	70.7903i		−	2.62186i
$28$	−16.7798			−0.599279
$29$			21.4524i			0.739739i	0.929084	+	0.369870i	$0.120598\pi$
$29$			21.4524i			0.739739i	−0.929084	+	0.369870i	$0.879402\pi$
$30$		0			0
$31$	24.9579			0.805093			0.402547	−	0.915400i	$-0.368125\pi$
$31$	24.9579			0.805093			0.402547	+	0.915400i	$0.368125\pi$
$32$	−44.3404			−1.38564
$33$	−59.4615	+	13.6630i	−1.80186	+	0.414030i
$34$	70.9092			2.08556
$35$		0			0
$36$	−81.4704			−2.26307
$37$			30.4659i			0.823403i	0.911319	+	0.411701i	$0.135065\pi$
$37$			30.4659i			0.823403i	−0.911319	+	0.411701i	$0.864935\pi$
$38$			23.5008i			0.618442i
$39$			87.1145i			2.23371i
$40$		0			0
$41$			10.5577i			0.257506i	0.991677	+	0.128753i	$0.0410974\pi$
$41$			10.5577i			0.257506i	−0.991677	+	0.128753i	$0.958903\pi$
$42$		−	69.1821i		−	1.64719i
$43$	68.3676			1.58994			0.794972	−	0.606645i	$-0.207485\pi$
$43$	68.3676			1.58994			0.794972	+	0.606645i	$0.207485\pi$
$44$	9.22164	+	40.1327i	0.209583	+	0.912106i
$45$		0			0
$46$		−	55.3397i		−	1.20304i
$47$			25.0636i			0.533269i	0.963798	+	0.266634i	$0.0859116\pi$
$47$			25.0636i			0.533269i	−0.963798	+	0.266634i	$0.914088\pi$
$48$		−	94.0690i		−	1.95977i
$49$	−28.9082			−0.589964
$50$		0			0
$51$			141.335i			2.77127i
$52$	58.7967			1.13071
$53$		−	93.9329i		−	1.77232i	−0.463381	−	0.886159i	$-0.653364\pi$
$53$		−	93.9329i		−	1.77232i	0.463381	−	0.886159i	$-0.346636\pi$
$54$		−	196.989i		−	3.64795i
$55$		0			0
$56$	3.19936			0.0571315
$57$	−46.8414			−0.821778
$58$			59.6960i			1.02924i
$59$	27.3730			0.463949			0.231974	−	0.972722i	$-0.425481\pi$
$59$	27.3730			0.463949			0.231974	+	0.972722i	$0.425481\pi$
$60$		0			0
$61$		−	81.1075i		−	1.32963i	−0.747008	−	0.664815i	$-0.768510\pi$
$61$		−	81.1075i		−	1.32963i	0.747008	−	0.664815i	$-0.231490\pi$
$62$	69.4507			1.12017
$63$	97.5509			1.54843
$64$	−55.5457			−0.867902
$65$		0			0
$66$	−165.464	+	38.0202i	−2.50703	+	0.576064i
$67$			49.5118i			0.738982i	0.929234	+	0.369491i	$0.120468\pi$
$67$			49.5118i			0.738982i	−0.929234	+	0.369491i	$0.879532\pi$
$68$	95.3920			1.40282
$69$	110.302			1.59858
$70$		0			0
$71$	44.0132			0.619904			0.309952	−	0.950752i	$-0.399687\pi$
$71$	44.0132			0.619904			0.309952	+	0.950752i	$0.399687\pi$
$72$	15.5338			0.215747
$73$	−29.1783			−0.399703			−0.199851	−	0.979826i	$-0.564046\pi$
$73$	−29.1783			−0.399703			−0.199851	+	0.979826i	$0.564046\pi$
$74$			84.7779i			1.14565i
$75$		0			0
$76$			31.6149i			0.415986i
$77$	−11.0418	−	48.0540i	−0.143400	−	0.624078i
$78$			242.415i			3.10788i
$79$		−	51.3920i		−	0.650532i	−0.945623	−	0.325266i	$-0.894546\pi$
$79$		−	51.3920i		−	0.650532i	0.945623	−	0.325266i	$-0.105454\pi$
$80$		0			0
$81$	196.767			2.42922
$82$			29.3792i			0.358283i
$83$	47.2115			0.568814			0.284407	−	0.958704i	$-0.408203\pi$
$83$	47.2115			0.568814			0.284407	+	0.958704i	$0.408203\pi$
$84$		−	93.0685i		−	1.10796i
$85$		0			0
$86$	190.248			2.21218
$87$	−118.985			−1.36764
$88$	−1.75827	−	7.65199i	−0.0199803	−	0.0869545i
$89$	−147.455			−1.65679			−0.828397	−	0.560141i	$-0.810747\pi$
$89$	−147.455			−1.65679			−0.828397	+	0.560141i	$0.810747\pi$
$90$		0			0
$91$	−70.4019			−0.773647
$92$		−	74.4468i		−	0.809205i
$93$			138.428i			1.48847i
$94$			69.7449i			0.741967i
$95$		0			0
$96$		−	245.932i		−	2.56179i
$97$		−	87.8176i		−	0.905337i	−0.891679	−	0.452668i	$-0.850472\pi$
$97$		−	87.8176i		−	0.905337i	0.891679	−	0.452668i	$-0.149528\pi$
$98$	−80.4433			−0.820850
$99$	−53.6108	−	233.315i	−0.541523	−	2.35671i
$100$		0			0
$101$		−	22.1571i		−	0.219377i	−0.993966	−	0.109688i	$-0.965015\pi$
$101$		−	22.1571i		−	0.219377i	0.993966	−	0.109688i	$-0.0349853\pi$
$102$			393.295i			3.85583i
$103$			64.5972i			0.627158i	0.949562	+	0.313579i	$0.101528\pi$
$103$			64.5972i			0.627158i	−0.949562	+	0.313579i	$0.898472\pi$
$104$	−11.2106			−0.107794
$105$		0			0
$106$		−	261.388i		−	2.46593i
$107$	−39.4535			−0.368725			−0.184362	−	0.982858i	$-0.559022\pi$
$107$	−39.4535			−0.368725			−0.184362	+	0.982858i	$0.559022\pi$
$108$		−	265.003i		−	2.45374i
$109$			12.6081i			0.115671i	0.998326	+	0.0578355i	$0.0184199\pi$
$109$			12.6081i			0.115671i	−0.998326	+	0.0578355i	$0.981580\pi$
$110$		0			0
$111$	−168.978			−1.52232
$112$	76.0222			0.678770
$113$		−	98.6045i		−	0.872606i	−0.899800	−	0.436303i	$-0.856288\pi$
$113$		−	98.6045i		−	0.872606i	0.899800	−	0.436303i	$-0.143712\pi$
$114$	−130.346			−1.14339
$115$		0			0
$116$			80.3072i			0.692304i
$117$	−341.820			−2.92154
$118$	76.1712			0.645519
$119$	−114.220			−0.959834
$120$		0			0
$121$	−108.864	+	52.8178i	−0.899699	+	0.436511i
$122$		−	225.699i		−	1.84999i
$123$	−58.5580			−0.476081
$124$	93.4299			0.753467
$125$		0			0
$126$	271.456			2.15441
$127$	155.235			1.22233			0.611163	−	0.791505i	$-0.290702\pi$
$127$	155.235			1.22233			0.611163	+	0.791505i	$0.290702\pi$
$128$	22.7935			0.178074
$129$			379.198i			2.93952i
$130$		0			0
$131$			103.068i			0.786778i	0.919372	+	0.393389i	$0.128698\pi$
$131$			103.068i			0.786778i	−0.919372	+	0.393389i	$0.871302\pi$
$132$	−222.594	+	51.1474i	−1.68632	+	0.387480i
$133$		−	37.8550i		−	0.284624i
$134$			137.777i			1.02819i
$135$		0			0
$136$	−18.1881			−0.133736
$137$		−	46.4667i		−	0.339173i	−0.985515	−	0.169587i	$-0.945757\pi$
$137$		−	46.4667i		−	0.339173i	0.985515	−	0.169587i	$-0.0542432\pi$
$138$	306.939			2.22420
$139$		−	113.716i		−	0.818102i	−0.912512	−	0.409051i	$-0.865860\pi$
$139$		−	113.716i		−	0.818102i	0.912512	−	0.409051i	$-0.134140\pi$
$140$		0			0
$141$	−139.014			−0.985917
$142$	122.476			0.862508
$143$	38.6906	+	168.382i	0.270564	+	1.17750i
$144$	369.108			2.56325
$145$		0			0
$146$	−81.1949			−0.556129
$147$		−	160.338i		−	1.09074i
$148$			114.049i			0.770602i
$149$		−	160.233i		−	1.07539i	−0.843139	−	0.537695i	$-0.819295\pi$
$149$		−	160.233i		−	1.07539i	0.843139	−	0.537695i	$-0.180705\pi$
$150$		0			0
$151$			166.134i			1.10023i	0.835090	+	0.550113i	$0.185415\pi$
$151$			166.134i			1.10023i	−0.835090	+	0.550113i	$0.814585\pi$
$152$		−	6.02793i		−	0.0396575i
$153$	−554.569			−3.62463
$154$	−30.7262	−	133.721i	−0.199521	−	0.868315i
$155$		0			0
$156$			326.113i			2.09047i
$157$		−	61.2202i		−	0.389937i	−0.980809	−	0.194969i	$-0.937539\pi$
$157$		−	61.2202i		−	0.389937i	0.980809	−	0.194969i	$-0.0624605\pi$
$158$		−	143.009i		−	0.905123i
$159$	520.994			3.27669
$160$		0			0
$161$			89.1410i			0.553671i
$162$	547.545			3.37991
$163$		−	134.800i		−	0.826995i	−0.910505	−	0.413498i	$-0.864307\pi$
$163$		−	134.800i		−	0.826995i	0.910505	−	0.413498i	$-0.135693\pi$
$164$			39.5229i			0.240993i
$165$		0			0
$166$	131.376			0.791423
$167$	241.427			1.44567			0.722835	−	0.691021i	$-0.242839\pi$
$167$	241.427			1.44567			0.722835	+	0.691021i	$0.242839\pi$
$168$			17.7451i			0.105626i
$169$	77.6893			0.459700
$170$		0			0
$171$		−	183.796i		−	1.07483i
$172$	255.934			1.48799
$173$	181.146			1.04708			0.523542	−	0.852000i	$-0.324610\pi$
$173$	181.146			1.04708			0.523542	+	0.852000i	$0.324610\pi$
$174$	−331.101			−1.90288
$175$		0			0
$176$	−41.7793	−	181.824i	−0.237383	−	1.03309i
$177$			151.823i			0.857757i
$178$	−410.324			−2.30519
$179$	−109.667			−0.612664			−0.306332	−	0.951925i	$-0.599102\pi$
$179$	−109.667			−0.612664			−0.306332	+	0.951925i	$0.599102\pi$
$180$		0			0
$181$	−98.6522			−0.545040			−0.272520	−	0.962150i	$-0.587857\pi$
$181$	−98.6522			−0.545040			−0.272520	+	0.962150i	$0.587857\pi$
$182$	−195.908			−1.07642
$183$	449.859			2.45825
$184$			14.1946i			0.0771445i
$185$		0			0
$186$			385.205i			2.07099i
$187$	62.7717	+	273.183i	0.335678	+	1.46087i
$188$			93.8257i			0.499073i
$189$			317.309i			1.67889i
$190$		0			0
$191$	−72.5260			−0.379717			−0.189859	−	0.981811i	$-0.560803\pi$
$191$	−72.5260			−0.379717			−0.189859	+	0.981811i	$0.560803\pi$
$192$		−	308.082i		−	1.60459i
$193$	−132.224			−0.685098			−0.342549	−	0.939500i	$-0.611290\pi$
$193$	−132.224			−0.685098			−0.342549	+	0.939500i	$0.611290\pi$
$194$		−	244.371i		−	1.25965i
$195$		0			0
$196$	−108.218			−0.552132
$197$	−295.931			−1.50219			−0.751095	−	0.660194i	$-0.770474\pi$
$197$	−295.931			−1.50219			−0.751095	+	0.660194i	$0.770474\pi$
$198$	−149.184	−	649.248i	−0.753452	−	3.27903i
$199$	−77.7266			−0.390586			−0.195293	−	0.980745i	$-0.562566\pi$
$199$	−77.7266			−0.390586			−0.195293	+	0.980745i	$0.562566\pi$
$200$		0			0
$201$	−274.615			−1.36624
$202$		−	61.6568i		−	0.305232i
$203$		−	96.1581i		−	0.473685i
$204$			529.087i			2.59356i
$205$		0			0
$206$			179.756i			0.872600i
$207$			432.803i			2.09084i
$208$	−266.383			−1.28069
$209$	−90.5387	+	20.8039i	−0.433199	+	0.0995401i
$210$		0			0
$211$		−	162.936i		−	0.772209i	−0.922455	−	0.386104i	$-0.873820\pi$
$211$		−	162.936i		−	0.772209i	0.922455	−	0.386104i	$-0.126180\pi$
$212$		−	351.638i		−	1.65867i
$213$			244.117i			1.14609i
$214$	−109.788			−0.513028
$215$		0			0
$216$			50.5275i			0.233924i
$217$	−111.871			−0.515534
$218$			35.0848i			0.160940i
$219$		−	161.836i		−	0.738978i
$220$		0			0
$221$	400.229			1.81099
$222$	−470.217			−2.11809
$223$		−	27.3536i		−	0.122662i	−0.998117	−	0.0613310i	$-0.980465\pi$
$223$		−	27.3536i		−	0.122662i	0.998117	−	0.0613310i	$-0.0195345\pi$
$224$	198.751			0.887279
$225$		0			0
$226$		−	274.388i		−	1.21411i
$227$	−69.9378			−0.308096			−0.154048	−	0.988063i	$-0.549231\pi$
$227$	−69.9378			−0.308096			−0.154048	+	0.988063i	$0.549231\pi$
$228$	−175.351			−0.769082
$229$	126.890			0.554103			0.277052	−	0.960855i	$-0.410643\pi$
$229$	126.890			0.554103			0.277052	+	0.960855i	$0.410643\pi$
$230$		0			0
$231$	266.529	−	61.2428i	1.15381	−	0.265120i
$232$		−	15.3120i		−	0.0659999i
$233$	−127.078			−0.545398			−0.272699	−	0.962099i	$-0.587916\pi$
$233$	−127.078			−0.545398			−0.272699	+	0.962099i	$0.587916\pi$
$234$	−951.187			−4.06490
$235$		0			0
$236$	102.471			0.434198
$237$	285.044			1.20272
$238$	−317.842			−1.33547
$239$			242.100i			1.01297i	0.862249	+	0.506485i	$0.169055\pi$
$239$			242.100i			1.01297i	−0.862249	+	0.506485i	$0.830945\pi$
$240$		0			0
$241$		−	118.029i		−	0.489748i	−0.969555	−	0.244874i	$-0.921253\pi$
$241$		−	118.029i		−	0.489748i	0.969555	−	0.244874i	$-0.0787466\pi$
$242$	−302.936	+	146.977i	−1.25180	+	0.607343i
$243$			454.245i			1.86932i
$244$		−	303.626i		−	1.24437i
$245$		0			0
$246$	−162.950			−0.662399
$247$			132.644i			0.537022i
$248$	−17.8140			−0.0718308
$249$			261.857i			1.05163i
$250$		0			0
$251$	−122.747			−0.489033			−0.244516	−	0.969645i	$-0.578629\pi$
$251$	−122.747			−0.489033			−0.244516	+	0.969645i	$0.578629\pi$
$252$	365.182			1.44913
$253$	213.201	−	48.9890i	0.842690	−	0.193632i
$254$	431.976			1.70069
$255$		0			0
$256$	285.611			1.11567
$257$			440.444i			1.71379i	0.515491	+	0.856895i	$0.327609\pi$
$257$			440.444i			1.71379i	−0.515491	+	0.856895i	$0.672391\pi$
$258$			1055.20i			4.08992i
$259$		−	136.560i		−	0.527258i
$260$		0			0
$261$		−	466.873i		−	1.78878i
$262$			286.809i			1.09469i
$263$	196.653			0.747729			0.373865	−	0.927483i	$-0.378032\pi$
$263$	196.653			0.747729			0.373865	+	0.927483i	$0.378032\pi$
$264$	42.4414	−	9.75215i	0.160763	−	0.0369399i
$265$		0			0
$266$		−	105.340i		−	0.396014i
$267$		−	817.851i		−	3.06311i
$268$			185.347i			0.691595i
$269$	−140.084			−0.520759			−0.260379	−	0.965506i	$-0.583848\pi$
$269$	−140.084			−0.520759			−0.260379	+	0.965506i	$0.583848\pi$
$270$		0			0
$271$			122.461i			0.451886i	0.974141	+	0.225943i	$0.0725463\pi$
$271$			122.461i			0.451886i	−0.974141	+	0.225943i	$0.927454\pi$
$272$	−432.180			−1.58890
$273$		−	390.481i		−	1.43033i
$274$		−	129.304i		−	0.471911i
$275$		0			0
$276$	412.916			1.49607
$277$	431.002			1.55596			0.777981	−	0.628287i	$-0.216244\pi$
$277$	431.002			1.55596			0.777981	+	0.628287i	$0.216244\pi$
$278$		−	316.440i		−	1.13827i
$279$	−543.162			−1.94682
$280$		0			0
$281$			401.798i			1.42989i	0.699182	+	0.714943i	$0.253548\pi$
$281$			401.798i			1.42989i	−0.699182	+	0.714943i	$0.746452\pi$
$282$	−386.837			−1.37176
$283$	−22.4597			−0.0793628			−0.0396814	−	0.999212i	$-0.512634\pi$
$283$	−22.4597			−0.0793628			−0.0396814	+	0.999212i	$0.512634\pi$
$284$	164.763			0.580153
$285$		0			0
$286$	107.665	+	468.559i	0.376451	+	1.63832i
$287$		−	47.3239i		−	0.164892i
$288$	964.986			3.35065
$289$	360.333			1.24683
$290$		0			0
$291$	487.077			1.67380
$292$	−109.229			−0.374072
$293$	−455.602			−1.55496			−0.777478	−	0.628911i	$-0.783501\pi$
$293$	−455.602			−1.55496			−0.777478	+	0.628911i	$0.783501\pi$
$294$		−	446.175i		−	1.51760i
$295$		0			0
$296$		−	21.7454i		−	0.0734643i
$297$	758.916	−	174.383i	2.55527	−	0.587148i
$298$		−	445.883i		−	1.49625i
$299$		−	312.351i		−	1.04465i
$300$		0			0
$301$	−306.450			−1.01811
$302$			462.304i			1.53081i
$303$	122.893			0.405588
$304$		−	143.234i		−	0.471163i
$305$		0			0
$306$	−1543.21			−5.04316
$307$	−312.438			−1.01771			−0.508857	−	0.860851i	$-0.669932\pi$
$307$	−312.438			−1.01771			−0.508857	+	0.860851i	$0.669932\pi$
$308$	−41.3350	−	179.890i	−0.134204	−	0.584059i
$309$	−358.286			−1.15950
$310$		0			0
$311$	−256.878			−0.825975			−0.412987	−	0.910737i	$-0.635515\pi$
$311$	−256.878			−0.825975			−0.412987	+	0.910737i	$0.635515\pi$
$312$		−	62.1792i		−	0.199292i
$313$		−	29.6563i		−	0.0947485i	−0.998877	−	0.0473742i	$-0.984915\pi$
$313$		−	29.6563i		−	0.0947485i	0.998877	−	0.0473742i	$-0.0150853\pi$
$314$		−	170.358i		−	0.542542i
$315$		0			0
$316$		−	192.386i		−	0.608817i
$317$			99.6748i			0.314431i	0.987564	+	0.157216i	$0.0502518\pi$
$317$			99.6748i			0.314431i	−0.987564	+	0.157216i	$0.949748\pi$
$318$	1449.78			4.55905
$319$	−229.984	+	52.8454i	−0.720952	+	0.165659i
$320$		0			0
$321$		−	218.827i		−	0.681705i
$322$			248.054i			0.770354i
$323$			215.203i			0.666262i
$324$	736.596			2.27344
$325$		0			0
$326$		−	375.111i		−	1.15065i
$327$	−69.9305			−0.213855
$328$		−	7.53573i		−	0.0229748i
$329$		−	112.345i		−	0.341474i
$330$		0			0
$331$	138.630			0.418820			0.209410	−	0.977828i	$-0.432846\pi$
$331$	138.630			0.418820			0.209410	+	0.977828i	$0.432846\pi$
$332$	176.736			0.532339
$333$		−	663.034i		−	1.99109i
$334$	671.822			2.01144
$335$		0			0
$336$			421.654i			1.25492i
$337$	504.040			1.49567			0.747834	−	0.663886i	$-0.231094\pi$
$337$	504.040			1.49567			0.747834	+	0.663886i	$0.231094\pi$
$338$	216.187			0.639607
$339$	546.905			1.61329
$340$		0			0
$341$	61.4806	+	267.564i	0.180295	+	0.784646i
$342$		−	511.452i		−	1.49547i
$343$	349.215			1.01812
$344$	−48.7983			−0.141856
$345$		0			0
$346$	504.076			1.45687
$347$	305.042			0.879083			0.439542	−	0.898222i	$-0.355141\pi$
$347$	305.042			0.879083			0.439542	+	0.898222i	$0.355141\pi$
$348$	−445.420			−1.27994
$349$		−	383.638i		−	1.09925i	−0.835412	−	0.549625i	$-0.814771\pi$
$349$		−	383.638i		−	1.09925i	0.835412	−	0.549625i	$-0.185229\pi$
$350$		0			0
$351$		−	1111.86i		−	3.16768i
$352$	−109.227	−	475.356i	−0.310304	−	1.35044i
$353$			571.115i			1.61789i	0.587884	+	0.808945i	$0.299961\pi$
$353$			571.115i			1.61789i	−0.587884	+	0.808945i	$0.700039\pi$
$354$			422.480i			1.19345i
$355$		0			0
$356$	−551.997			−1.55055
$357$		−	633.517i		−	1.77456i
$358$	−305.172			−0.852434
$359$			105.966i			0.295169i	0.989049	+	0.147585i	$0.0471499\pi$
$359$			105.966i			0.295169i	−0.989049	+	0.147585i	$0.952850\pi$
$360$		0			0
$361$	289.677			0.802430
$362$	−274.521			−0.758345
$363$	−292.952	−	603.807i	−0.807029	−	1.66338i
$364$	−263.550			−0.724037
$365$		0			0
$366$	1251.83			3.42030
$367$		−	409.176i		−	1.11492i	−0.830203	−	0.557461i	$-0.811776\pi$
$367$		−	409.176i		−	1.11492i	0.830203	−	0.557461i	$-0.188224\pi$
$368$			337.287i			0.916540i
$369$		−	229.770i		−	0.622682i
$370$		0			0
$371$			421.043i			1.13489i
$372$			518.205i			1.39302i
$373$	286.691			0.768608			0.384304	−	0.923207i	$-0.374441\pi$
$373$	286.691			0.768608			0.384304	+	0.923207i	$0.374441\pi$
$374$	174.676	+	760.191i	0.467048	+	2.03260i
$375$		0			0
$376$		−	17.8895i		−	0.0475785i
$377$			336.939i			0.893738i
$378$			882.981i			2.33593i
$379$	396.663			1.04660			0.523302	−	0.852147i	$-0.324700\pi$
$379$	396.663			1.04660			0.523302	+	0.852147i	$0.324700\pi$
$380$		0			0
$381$			861.006i			2.25986i
$382$	−201.819			−0.528322
$383$			423.356i			1.10537i	0.833391	+	0.552684i	$0.186396\pi$
$383$			423.356i			1.10537i	−0.833391	+	0.552684i	$0.813604\pi$
$384$			126.423i			0.329227i
$385$		0			0
$386$	−367.941			−0.953216
$387$	−1487.90			−3.84469
$388$		−	328.745i		−	0.847282i
$389$	453.620			1.16612			0.583059	−	0.812430i	$-0.301855\pi$
$389$	453.620			1.16612			0.583059	+	0.812430i	$0.301855\pi$
$390$		0			0
$391$		−	506.760i		−	1.29606i
$392$	20.6336			0.0526368
$393$	−571.662			−1.45461
$394$	−823.493			−2.09008
$395$		0			0
$396$	−200.692	−	873.414i	−0.506798	−	2.20559i
$397$		−	535.740i		−	1.34947i	−0.738060	−	0.674735i	$-0.764258\pi$
$397$		−	535.740i		−	1.34947i	0.738060	−	0.674735i	$-0.235742\pi$
$398$	−216.291			−0.543445
$399$	209.961			0.526218
$400$		0			0
$401$	−611.297			−1.52443			−0.762216	−	0.647323i	$-0.775889\pi$
$401$	−611.297			−1.52443			−0.762216	+	0.647323i	$0.775889\pi$
$402$	−764.175			−1.90093
$403$	391.997			0.972698
$404$		−	82.9450i		−	0.205309i
$405$		0			0
$406$		−	267.581i		−	0.659066i
$407$	−326.613	+	75.0489i	−0.802490	+	0.184395i
$408$		−	100.880i		−	0.247254i
$409$		−	748.695i		−	1.83055i	−0.402831	−	0.915275i	$-0.631974\pi$
$409$		−	748.695i		−	1.83055i	0.402831	−	0.915275i	$-0.368026\pi$
$410$		0			0
$411$	257.725			0.627069
$412$			241.820i			0.586941i
$413$	−122.696			−0.297085
$414$			1204.37i			2.90910i
$415$		0			0
$416$	−696.425			−1.67410
$417$	630.721			1.51252
$418$	−251.943	+	57.8913i	−0.602735	+	0.138496i
$419$	−1.63966			−0.00391327			−0.00195663	−	0.999998i	$-0.500623\pi$
$419$	−1.63966			−0.00391327			−0.00195663	+	0.999998i	$0.500623\pi$
$420$		0			0
$421$	587.016			1.39434			0.697169	−	0.716907i	$-0.254443\pi$
$421$	587.016			1.39434			0.697169	+	0.716907i	$0.254443\pi$
$422$		−	453.404i		−	1.07442i
$423$		−	545.464i		−	1.28951i
$424$			67.0459i			0.158127i
$425$		0			0
$426$			679.308i			1.59462i
$427$			363.555i			0.851417i
$428$	−147.694			−0.345080
$429$	−933.922	+	214.596i	−2.17697	+	0.500223i
$430$		0			0
$431$		−	709.692i		−	1.64662i	−0.567595	−	0.823308i	$-0.692126\pi$
$431$		−	709.692i		−	1.64662i	0.567595	−	0.823308i	$-0.307874\pi$
$432$			1200.62i			2.77921i
$433$		−	821.863i		−	1.89807i	−0.315175	−	0.949034i	$-0.602063\pi$
$433$		−	821.863i		−	1.89807i	0.315175	−	0.949034i	$-0.397937\pi$
$434$	−311.305			−0.717292
$435$		0			0
$436$			47.1986i			0.108254i
$437$	167.951			0.384327
$438$		−	450.344i		−	1.02818i
$439$			522.233i			1.18960i	0.803875	+	0.594798i	$0.202768\pi$
$439$			522.233i			1.18960i	−0.803875	+	0.594798i	$0.797232\pi$
$440$		0			0
$441$	629.134			1.42661
$442$	1113.72			2.51974
$443$		−	377.862i		−	0.852963i	−0.904496	−	0.426481i	$-0.859753\pi$
$443$		−	377.862i		−	0.852963i	0.904496	−	0.426481i	$-0.140247\pi$
$444$	−632.568			−1.42470
$445$		0			0
$446$		−	76.1173i		−	0.170667i
$447$	888.726			1.98820
$448$	248.977			0.555753
$449$	−565.531			−1.25953			−0.629767	−	0.776784i	$-0.716850\pi$
$449$	−565.531			−1.25953			−0.629767	+	0.776784i	$0.716850\pi$
$450$		0			0
$451$	−113.186	+	26.0077i	−0.250966	+	0.0576667i
$452$		−	369.126i		−	0.816650i
$453$	−921.455			−2.03412
$454$	−194.617			−0.428672
$455$		0			0
$456$	33.4337			0.0733194
$457$	−311.699			−0.682054			−0.341027	−	0.940054i	$-0.610775\pi$
$457$	−311.699			−0.682054			−0.341027	+	0.940054i	$0.610775\pi$
$458$	353.098			0.770955
$459$		−	1803.88i		−	3.93002i
$460$		0			0
$461$			125.484i			0.272200i	0.990695	+	0.136100i	$0.0434569\pi$
$461$			125.484i			0.272200i	−0.990695	+	0.136100i	$0.956543\pi$
$462$	741.675	−	170.421i	1.60536	−	0.368877i
$463$			478.622i			1.03374i	0.856063	+	0.516871i	$0.172903\pi$
$463$			478.622i			1.03374i	−0.856063	+	0.516871i	$0.827097\pi$
$464$		−	363.838i		−	0.784133i
$465$		0			0
$466$	−353.621			−0.758844
$467$			422.419i			0.904538i	0.891882	+	0.452269i	$0.149385\pi$
$467$			422.419i			0.904538i	−0.891882	+	0.452269i	$0.850615\pi$
$468$	−1279.60			−2.73419
$469$		−	221.931i		−	0.473200i
$470$		0			0
$471$	339.555			0.720923
$472$	−19.5378			−0.0413937
$473$	168.415	+	732.944i	0.356057	+	1.54956i
$474$	793.195			1.67341
$475$		0			0
$476$	−427.584			−0.898285
$477$			2044.28i			4.28569i
$478$			673.695i			1.40940i
$479$			158.064i			0.329987i	0.986295	+	0.164993i	$0.0527603\pi$
$479$			158.064i			0.329987i	−0.986295	+	0.164993i	$0.947240\pi$
$480$		0			0
$481$			478.508i			0.994819i
$482$		−	328.442i		−	0.681414i
$483$	−494.417			−1.02364
$484$	−407.531	+	197.724i	−0.842006	+	0.408520i
$485$		0			0
$486$			1264.03i			2.60089i
$487$		−	840.800i		−	1.72649i	−0.504786	−	0.863245i	$-0.668429\pi$
$487$		−	840.800i		−	1.72649i	0.504786	−	0.863245i	$-0.331571\pi$
$488$			57.8916i			0.118630i
$489$	747.663			1.52896
$490$		0			0
$491$		−	327.239i		−	0.666476i	−0.942843	−	0.333238i	$-0.891859\pi$
$491$		−	327.239i		−	0.666476i	0.942843	−	0.333238i	$-0.108141\pi$
$492$	−219.212			−0.445553
$493$			546.651i			1.10883i
$494$			369.112i			0.747190i
$495$		0			0
$496$	−423.291			−0.853409
$497$	−197.284			−0.396950
$498$			728.673i			1.46320i
$499$	−551.123			−1.10445			−0.552227	−	0.833693i	$-0.686222\pi$
$499$	−551.123			−1.10445			−0.552227	+	0.833693i	$0.686222\pi$
$500$		0			0
$501$			1339.06i			2.67278i
$502$	−341.571			−0.680420
$503$	−399.050			−0.793340			−0.396670	−	0.917961i	$-0.629834\pi$
$503$	−399.050			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$504$	−69.6283			−0.138151
$505$		0			0
$506$	593.276	−	136.322i	1.17248	−	0.269412i
$507$			430.900i			0.849901i
$508$	581.124			1.14394
$509$	18.2410			0.0358370			0.0179185	−	0.999839i	$-0.494296\pi$
$509$	18.2410			0.0358370			0.0179185	+	0.999839i	$0.494296\pi$
$510$		0			0
$511$	130.788			0.255946
$512$	703.599			1.37422
$513$	597.844			1.16539
$514$			1225.63i			2.38449i
$515$		0			0
$516$			1419.53i			2.75102i
$517$	−268.698	+	61.7411i	−0.519725	+	0.119422i
$518$		−	380.007i		−	0.733605i
$519$			1004.72i			1.93587i
$520$		0			0
$521$	673.198			1.29213			0.646064	−	0.763284i	$-0.276414\pi$
$521$	673.198			1.29213			0.646064	+	0.763284i	$0.276414\pi$
$522$		−	1299.17i		−	2.48884i
$523$	102.262			0.195529			0.0977645	−	0.995210i	$-0.468831\pi$
$523$	102.262			0.195529			0.0977645	+	0.995210i	$0.468831\pi$
$524$			385.835i			0.736326i
$525$		0			0
$526$	547.229			1.04036
$527$	635.977			1.20679
$528$	1008.48	−	231.727i	1.91000	−	0.438877i
$529$	133.509			0.252380
$530$		0			0
$531$	−595.723			−1.12189
$532$		−	141.710i		−	0.266373i
$533$			165.824i			0.311114i
$534$		−	2275.84i		−	4.26188i
$535$		0			0
$536$		−	35.3397i		−	0.0659323i
$537$		−	608.262i		−	1.13270i
$538$	−389.814			−0.724561
$539$	−71.2117	−	309.914i	−0.132118	−	0.574980i
$540$		0			0
$541$			822.873i			1.52102i	0.649324	+	0.760512i	$0.275052\pi$
$541$			822.873i			1.52102i	−0.649324	+	0.760512i	$0.724948\pi$
$542$			340.774i			0.628735i
$543$		−	547.170i		−	1.00768i
$544$	−1129.88			−2.07699
$545$		0			0
$546$		−	1086.60i		−	1.99010i
$547$	−641.446			−1.17266			−0.586331	−	0.810071i	$-0.699428\pi$
$547$	−641.446			−1.17266			−0.586331	+	0.810071i	$0.699428\pi$
$548$		−	173.948i		−	0.317424i
$549$			1765.15i			3.21522i
$550$		0			0
$551$	−181.172			−0.328805
$552$	−78.7296			−0.142626
$553$			230.359i			0.416562i
$554$	1199.35			2.16490
$555$		0			0
$556$		−	425.696i		−	0.765641i
$557$	523.719			0.940250			0.470125	−	0.882600i	$-0.344209\pi$
$557$	523.719			0.940250			0.470125	+	0.882600i	$0.344209\pi$
$558$	−1511.47			−2.70872
$559$	1073.81			1.92094
$560$		0			0
$561$	−1515.20	+	348.161i	−2.70089	+	0.620607i
$562$			1118.09i			1.98948i
$563$	−1008.31			−1.79095			−0.895475	−	0.445111i	$-0.853164\pi$
$563$	−1008.31			−1.79095			−0.895475	+	0.445111i	$0.853164\pi$
$564$	−520.400			−0.922695
$565$		0			0
$566$	−62.4988			−0.110422
$567$	−881.984			−1.55553
$568$	−31.4150			−0.0553081
$569$			369.577i			0.649521i	0.945796	+	0.324760i	$0.105284\pi$
$569$			369.577i			0.649521i	−0.945796	+	0.324760i	$0.894716\pi$
$570$		0			0
$571$		−	456.385i		−	0.799273i	−0.916674	−	0.399636i	$-0.869136\pi$
$571$		−	456.385i		−	0.799273i	0.916674	−	0.399636i	$-0.130864\pi$
$572$	144.838	+	630.338i	0.253214	+	1.10199i
$573$		−	402.262i		−	0.702028i
$574$		−	131.689i		−	0.229423i
$575$		0			0
$576$	1208.85			2.09870
$577$		−	886.043i		−	1.53560i	−0.640687	−	0.767802i	$-0.721351\pi$
$577$		−	886.043i		−	1.53560i	0.640687	−	0.767802i	$-0.278649\pi$
$578$	1002.70			1.73478
$579$		−	733.373i		−	1.26662i
$580$		0			0
$581$	−211.620			−0.364235
$582$	1355.40			2.32886
$583$	1007.02	−	231.392i	1.72731	−	0.396898i
$584$	20.8264			0.0356617
$585$		0			0
$586$	−1267.81			−2.16350
$587$		−	497.919i		−	0.848243i	−0.905605	−	0.424121i	$-0.860583\pi$
$587$		−	497.919i		−	0.848243i	0.905605	−	0.424121i	$-0.139417\pi$
$588$		−	600.226i		−	1.02079i
$589$			210.776i			0.357855i
$590$		0			0
$591$		−	1641.37i		−	2.77728i
$592$		−	516.708i		−	0.872817i
$593$	60.1067			0.101360			0.0506802	−	0.998715i	$-0.483861\pi$
$593$	60.1067			0.101360			0.0506802	+	0.998715i	$0.483861\pi$
$594$	2111.85	−	485.258i	3.55530	−	0.816933i
$595$		0			0
$596$		−	599.833i		−	1.00643i
$597$		−	431.107i		−	0.722122i
$598$		−	869.185i		−	1.45349i
$599$	−935.800			−1.56227			−0.781135	−	0.624362i	$-0.785359\pi$
$599$	−935.800			−1.56227			−0.781135	+	0.624362i	$0.785359\pi$
$600$		0			0
$601$		−	925.265i		−	1.53954i	−0.638320	−	0.769771i	$-0.720370\pi$
$601$		−	925.265i		−	1.53954i	0.638320	−	0.769771i	$-0.279630\pi$
$602$	−852.763			−1.41655
$603$		−	1077.53i		−	1.78695i
$604$			621.923i			1.02967i
$605$		0			0
$606$	341.976			0.564318
$607$	790.264			1.30192			0.650959	−	0.759113i	$-0.274367\pi$
$607$	790.264			1.30192			0.650959	+	0.759113i	$0.274367\pi$
$608$		−	374.467i		−	0.615899i
$609$	533.337			0.875758
$610$		0			0
$611$			393.658i			0.644285i
$612$	−2076.03			−3.39221
$613$	−390.665			−0.637300			−0.318650	−	0.947872i	$-0.603230\pi$
$613$	−390.665			−0.637300			−0.318650	+	0.947872i	$0.603230\pi$
$614$	−869.427			−1.41600
$615$		0			0
$616$	7.88123	+	34.2992i	0.0127942	+	0.0556805i
$617$			283.723i			0.459843i	0.973209	+	0.229922i	$0.0738470\pi$
$617$			283.723i			0.459843i	−0.973209	+	0.229922i	$0.926153\pi$
$618$	−997.007			−1.61328
$619$	774.717			1.25156			0.625781	−	0.779999i	$-0.284780\pi$
$619$	774.717			1.25156			0.625781	+	0.779999i	$0.284780\pi$
$620$		0			0
$621$	−1407.80			−2.26699
$622$	−714.818			−1.14923
$623$	660.949			1.06091
$624$		−	1477.48i		−	2.36776i
$625$		0			0
$626$		−	82.5250i		−	0.131829i
$627$	−115.388	−	502.169i	−0.184032	−	0.800907i
$628$		−	229.178i		−	0.364933i
$629$			776.332i			1.23423i
$630$		0			0
$631$	392.301			0.621712			0.310856	−	0.950457i	$-0.399384\pi$
$631$	392.301			0.621712			0.310856	+	0.950457i	$0.399384\pi$
$632$			36.6818i			0.0580408i
$633$	903.717			1.42767
$634$			277.366i			0.437487i
$635$		0			0
$636$	1950.34			3.06658
$637$	−454.042			−0.712782
$638$	−639.979	+	147.054i	−1.00310	+	0.230492i
$639$	−957.865			−1.49901
$640$		0			0
$641$	−685.356			−1.06920			−0.534599	−	0.845106i	$-0.679537\pi$
$641$	−685.356			−1.06920			−0.534599	+	0.845106i	$0.679537\pi$
$642$		−	608.934i		−	0.948495i
$643$			747.072i			1.16185i	0.813956	+	0.580927i	$0.197310\pi$
$643$			747.072i			1.16185i	−0.813956	+	0.580927i	$0.802690\pi$
$644$			333.699i			0.518167i
$645$		0			0
$646$			598.848i			0.927009i
$647$			190.791i			0.294885i	0.989071	+	0.147443i	$0.0471042\pi$
$647$			190.791i			0.294885i	−0.989071	+	0.147443i	$0.952896\pi$
$648$	−140.445			−0.216736
$649$	67.4299	+	293.456i	0.103898	+	0.452166i
$650$		0			0
$651$		−	620.487i		−	0.953129i
$652$		−	504.625i		−	0.773964i
$653$			142.136i			0.217666i	0.994060	+	0.108833i	$0.0347114\pi$
$653$			142.136i			0.217666i	−0.994060	+	0.108833i	$0.965289\pi$
$654$	−194.596			−0.297548
$655$		0			0
$656$		−	179.061i		−	0.272959i
$657$	635.012			0.966533
$658$		−	312.624i		−	0.475112i
$659$			528.247i			0.801589i	0.916168	+	0.400794i	$0.131266\pi$
$659$			528.247i			0.801589i	−0.916168	+	0.400794i	$0.868734\pi$
$660$		0			0
$661$	2.43838			0.00368892			0.00184446	−	0.999998i	$-0.499413\pi$
$661$	2.43838			0.00368892			0.00184446	+	0.999998i	$0.499413\pi$
$662$	385.766			0.582729
$663$			2219.85i			3.34820i
$664$	−33.6979			−0.0507498
$665$		0			0
$666$		−	1845.03i		−	2.77032i
$667$	426.624			0.639616
$668$	903.781			1.35297
$669$	151.716			0.226780
$670$		0			0
$671$	869.523	−	199.798i	1.29586	−	0.297762i
$672$			1102.36i			1.64042i
$673$	684.594			1.01723			0.508614	−	0.860995i	$-0.330158\pi$
$673$	684.594			1.01723			0.508614	+	0.860995i	$0.330158\pi$
$674$	1402.60			2.08101
$675$		0			0
$676$	290.830			0.430222
$677$	−326.416			−0.482151			−0.241076	−	0.970506i	$-0.577500\pi$
$677$	−326.416			−0.482151			−0.241076	+	0.970506i	$0.577500\pi$
$678$	1521.88			2.24466
$679$			393.633i			0.579724i
$680$		0			0
$681$		−	387.907i		−	0.569614i
$682$	171.083	+	744.555i	0.250855	+	1.09172i
$683$			1162.56i			1.70213i	0.525058	+	0.851067i	$0.324044\pi$
$683$			1162.56i			1.70213i	−0.525058	+	0.851067i	$0.675956\pi$
$684$		−	688.040i		−	1.00591i
$685$		0			0
$686$	971.765			1.41657
$687$			703.787i			1.02444i
$688$	−1159.53			−1.68536
$689$		−	1475.34i		−	2.14128i
$690$		0			0
$691$	−400.519			−0.579623			−0.289811	−	0.957084i	$-0.593593\pi$
$691$	−400.519			−0.579623			−0.289811	+	0.957084i	$0.593593\pi$
$692$	678.118			0.979940
$693$	240.304	+	1045.81i	0.346759	+	1.50910i
$694$	848.845			1.22312
$695$		0			0
$696$	84.9271			0.122022
$697$			269.032i			0.385986i
$698$		−	1067.55i		−	1.52945i
$699$		−	704.831i		−	1.00834i
$700$		0			0
$701$			819.099i			1.16847i	0.811584	+	0.584236i	$0.198606\pi$
$701$			819.099i			1.16847i	−0.811584	+	0.584236i	$0.801394\pi$
$702$		−	3093.98i		−	4.40738i
$703$	−257.293			−0.365993
$704$	−136.830	−	595.485i	−0.194361	−	0.845859i
$705$		0			0
$706$			1589.25i			2.25106i
$707$			99.3165i			0.140476i
$708$			568.350i			0.802754i
$709$	−516.432			−0.728395			−0.364198	−	0.931322i	$-0.618657\pi$
$709$	−516.432			−0.728395			−0.364198	+	0.931322i	$0.618657\pi$
$710$		0			0
$711$			1118.45i			1.57307i
$712$	105.248			0.147820
$713$		−	496.336i		−	0.696124i
$714$		−	1762.90i		−	2.46904i
$715$		0			0
$716$	−410.538			−0.573377
$717$	−1342.80			−1.87280
$718$			294.873i			0.410686i
$719$	−382.550			−0.532058			−0.266029	−	0.963965i	$-0.585712\pi$
$719$	−382.550			−0.532058			−0.266029	+	0.963965i	$0.585712\pi$
$720$		0			0
$721$		−	289.550i		−	0.401595i
$722$	806.089			1.11647
$723$	654.644			0.905455
$724$	−369.305			−0.510089
$725$		0			0
$726$	−815.201	−	1680.22i	−1.12287	−	2.31436i
$727$			890.685i			1.22515i	0.790412	+	0.612575i	$0.209866\pi$
$727$			890.685i			1.22515i	−0.790412	+	0.612575i	$0.790134\pi$
$728$	50.2503			0.0690252
$729$	−748.548			−1.02681
$730$		0			0
$731$	1742.15			2.38324
$732$	1684.05			2.30061
$733$	17.9184			0.0244454			0.0122227	−	0.999925i	$-0.496109\pi$
$733$	17.9184			0.0244454			0.0122227	+	0.999925i	$0.496109\pi$
$734$		−	1138.62i		−	1.55126i
$735$		0			0
$736$			881.795i			1.19809i
$737$	−530.797	+	121.966i	−0.720214	+	0.165490i
$738$		−	639.384i		−	0.866374i
$739$			765.890i			1.03639i	0.855263	+	0.518194i	$0.173395\pi$
$739$			765.890i			1.03639i	−0.855263	+	0.518194i	$0.826605\pi$
$740$		0			0
$741$	−735.706			−0.992856
$742$			1171.64i			1.57903i
$743$	402.876			0.542229			0.271114	−	0.962547i	$-0.412608\pi$
$743$	402.876			0.542229			0.271114	+	0.962547i	$0.412608\pi$
$744$		−	98.8047i		−	0.132802i
$745$		0			0
$746$	797.779			1.06941
$747$	−1027.47			−1.37547
$748$	234.986	+	1022.66i	0.314152	+	1.36719i
$749$	176.846			0.236109
$750$		0			0
$751$	−884.758			−1.17811			−0.589053	−	0.808094i	$-0.700499\pi$
$751$	−884.758			−1.17811			−0.589053	+	0.808094i	$0.700499\pi$
$752$		−	425.084i		−	0.565272i
$753$		−	680.812i		−	0.904133i
$754$			937.606i			1.24351i
$755$		0			0
$756$			1187.85i			1.57123i
$757$			752.068i			0.993485i	0.867898	+	0.496742i	$0.165471\pi$
$757$			752.068i			0.993485i	−0.867898	+	0.496742i	$0.834529\pi$
$758$	1103.80			1.45620
$759$	271.715	+	1182.51i	0.357991	+	1.55798i
$760$		0			0
$761$		−	876.298i		−	1.15151i	−0.817623	−	0.575754i	$-0.804708\pi$
$761$		−	876.298i		−	1.15151i	0.817623	−	0.575754i	$-0.195292\pi$
$762$			2395.93i			3.14427i
$763$		−	56.5145i		−	0.0740689i
$764$	−271.501			−0.355368
$765$		0			0
$766$			1178.08i			1.53796i
$767$	429.930			0.560534
$768$			1584.13i			2.06267i
$769$		−	794.557i		−	1.03323i	−0.856217	−	0.516617i	$-0.827191\pi$
$769$		−	794.557i		−	1.03323i	0.856217	−	0.516617i	$-0.172809\pi$
$770$		0			0
$771$	−2442.90			−3.16849
$772$	−494.980			−0.641166
$773$		−	911.736i		−	1.17948i	−0.807594	−	0.589738i	$-0.799231\pi$
$773$		−	911.736i		−	1.17948i	0.807594	−	0.589738i	$-0.200769\pi$
$774$	−4140.39			−5.34934
$775$		0			0
$776$			62.6810i			0.0807745i
$777$	757.423			0.974805
$778$	1262.30			1.62249
$779$	−89.1631			−0.114458
$780$		0			0
$781$	108.421	+	471.849i	0.138823	+	0.604160i
$782$		−	1410.17i		−	1.80328i
$783$	1518.62			1.93949
$784$	490.289			0.625369
$785$		0			0
$786$	−1590.77			−2.02388
$787$	−1566.53			−1.99050			−0.995252	−	0.0973313i	$-0.968969\pi$
$787$	−1566.53			−1.99050			−0.995252	+	0.0973313i	$0.968969\pi$
$788$	−1107.82			−1.40586
$789$			1090.73i			1.38242i
$790$		0			0
$791$			441.983i			0.558765i
$792$	38.2654	+	166.532i	0.0483149	+	0.210267i
$793$		−	1273.90i		−	1.60643i
$794$		−	1490.81i		−	1.87760i
$795$		0			0
$796$	−290.970			−0.365540
$797$			488.561i			0.613001i	0.951871	+	0.306500i	$0.0991580\pi$
$797$			488.561i			0.613001i	−0.951871	+	0.306500i	$0.900842\pi$
$798$	584.262			0.732158
$799$			638.672i			0.799339i
$800$		0			0
$801$	3209.08			4.00634
$802$	−1701.07			−2.12103
$803$	−71.8771	−	312.810i	−0.0895107	−	0.389551i
$804$	−1028.02			−1.27863
$805$		0			0
$806$	1090.82			1.35337
$807$		−	776.970i		−	0.962788i
$808$			15.8149i			0.0195729i
$809$			177.955i			0.219969i	0.993933	+	0.109984i	$0.0350801\pi$
$809$			177.955i			0.219969i	−0.993933	+	0.109984i	$0.964920\pi$
$810$		0			0
$811$			148.090i			0.182602i	0.995823	+	0.0913009i	$0.0291025\pi$
$811$			148.090i			0.182602i	−0.995823	+	0.0913009i	$0.970897\pi$
$812$		−	359.968i		−	0.443310i
$813$	−679.225			−0.835455
$814$	−908.872	+	208.840i	−1.11655	+	0.256560i
$815$		0			0
$816$		−	2397.07i		−	2.93758i
$817$			577.384i			0.706712i
$818$		−	2083.40i		−	2.54695i
$819$	1532.17			1.87078
$820$		0			0
$821$			95.9583i			0.116880i	0.998291	+	0.0584399i	$0.0186126\pi$
$821$			95.9583i			0.116880i	−0.998291	+	0.0584399i	$0.981387\pi$
$822$	717.177			0.872478
$823$			780.102i			0.947876i	0.880558	+	0.473938i	$0.157168\pi$
$823$			780.102i			0.947876i	−0.880558	+	0.473938i	$0.842832\pi$
$824$		−	46.1072i		−	0.0559553i
$825$		0			0
$826$	−341.429			−0.413352
$827$	51.5115			0.0622872			0.0311436	−	0.999515i	$-0.490085\pi$
$827$	51.5115			0.0622872			0.0311436	+	0.999515i	$0.490085\pi$
$828$			1620.20i			1.95676i
$829$	1102.12			1.32945			0.664726	−	0.747087i	$-0.268548\pi$
$829$	1102.12			1.32945			0.664726	+	0.747087i	$0.268548\pi$
$830$		0			0
$831$			2390.53i			2.87669i
$832$	−872.421			−1.04858
$833$	−736.640			−0.884321
$834$	1755.12			2.10446
$835$		0			0
$836$	−338.932	+	77.8793i	−0.405421	+	0.0931571i
$837$		−	1766.78i		−	2.11084i
$838$	−4.56271			−0.00544476
$839$	−727.457			−0.867052			−0.433526	−	0.901141i	$-0.642731\pi$
$839$	−727.457			−0.867052			−0.433526	+	0.901141i	$0.642731\pi$
$840$		0			0
$841$	380.793			0.452786
$842$	1633.50			1.94002
$843$	−2228.56			−2.64360
$844$		−	609.951i		−	0.722691i
$845$		0			0
$846$		−	1517.87i		−	1.79417i
$847$	487.969	−	236.750i	0.576114	−	0.279516i
$848$			1593.12i			1.87868i
$849$		−	124.571i		−	0.146727i
$850$		0			0
$851$	605.874			0.711955
$852$			913.852i			1.07260i
$853$	−942.330			−1.10472			−0.552362	−	0.833604i	$-0.686274\pi$
$853$	−942.330			−1.10472			−0.552362	+	0.833604i	$0.686274\pi$
$854$			1011.67i			1.18463i
$855$		0			0
$856$	28.1605			0.0328978
$857$	−584.440			−0.681960			−0.340980	−	0.940070i	$-0.610759\pi$
$857$	−584.440			−0.681960			−0.340980	+	0.940070i	$0.610759\pi$
$858$	−2598.84	+	597.158i	−3.02895	+	0.695989i
$859$	−209.717			−0.244141			−0.122070	−	0.992521i	$-0.538953\pi$
$859$	−209.717			−0.244141			−0.122070	+	0.992521i	$0.538953\pi$
$860$		0			0
$861$	262.480			0.304854
$862$		−	1974.87i		−	2.29103i
$863$		−	1655.39i		−	1.91818i	−0.283101	−	0.959090i	$-0.591363\pi$
$863$		−	1655.39i		−	1.91818i	0.283101	−	0.959090i	$-0.408637\pi$
$864$			3138.87i			3.63295i
$865$		0			0
$866$		−	2287.01i		−	2.64089i
$867$			1998.57i			2.30516i
$868$	−418.789			−0.482476
$869$	550.955	−	126.598i	0.634010	−	0.145682i
$870$		0			0
$871$			777.649i			0.892824i
$872$		−	8.99923i		−	0.0103202i
$873$			1911.19i			2.18922i
$874$	467.359			0.534736
$875$		0			0
$876$		−	605.834i		−	0.691591i
$877$	−265.595			−0.302845			−0.151422	−	0.988469i	$-0.548385\pi$
$877$	−265.595			−0.302845			−0.151422	+	0.988469i	$0.548385\pi$
$878$			1453.22i			1.65515i
$879$		−	2526.98i		−	2.87483i
$880$		0			0
$881$	187.558			0.212892			0.106446	−	0.994319i	$-0.466053\pi$
$881$	187.558			0.212892			0.106446	+	0.994319i	$0.466053\pi$
$882$	1750.70			1.98492
$883$			36.3595i			0.0411773i	0.999788	+	0.0205886i	$0.00655403\pi$
$883$			36.3595i			0.0411773i	−0.999788	+	0.0205886i	$0.993446\pi$
$884$	1498.26			1.69486
$885$		0			0
$886$		−	1051.48i		−	1.18678i
$887$	−666.369			−0.751261			−0.375631	−	0.926769i	$-0.622574\pi$
$887$	−666.369			−0.751261			−0.375631	+	0.926769i	$0.622574\pi$
$888$	120.610			0.135822
$889$	−695.825			−0.782705
$890$		0			0
$891$	484.710	+	2109.46i	0.544006	+	2.36752i
$892$		−	102.398i		−	0.114796i
$893$	−211.669			−0.237032
$894$	2473.07			2.76630
$895$		0			0
$896$	−102.169			−0.114028
$897$	1732.44			1.93137
$898$	−1573.71			−1.75246
$899$			535.408i			0.595559i
$900$		0			0
$901$		−	2393.60i		−	2.65660i
$902$	−314.963	+	72.3719i	−0.349183	+	0.0802349i
$903$		−	1699.71i		−	1.88229i
$904$			70.3803i			0.0778543i
$905$		0			0
$906$	−2564.15			−2.83018
$907$		−	667.718i		−	0.736182i	−0.929790	−	0.368091i	$-0.880011\pi$
$907$		−	667.718i		−	0.736182i	0.929790	−	0.368091i	$-0.119989\pi$
$908$	−261.812			−0.288339
$909$			482.208i			0.530481i
$910$		0			0
$911$	218.396			0.239732			0.119866	−	0.992790i	$-0.461754\pi$
$911$	218.396			0.239732			0.119866	+	0.992790i	$0.461754\pi$
$912$	794.439			0.871095
$913$	116.300	+	506.137i	0.127382	+	0.554367i
$914$	−867.368			−0.948981
$915$		0			0
$916$	475.011			0.518571
$917$		−	461.990i		−	0.503806i
$918$		−	5019.68i		−	5.46806i
$919$			197.616i			0.215034i	0.994203	+	0.107517i	$0.0342900\pi$
$919$			197.616i			0.215034i	−0.994203	+	0.107517i	$0.965710\pi$
$920$		0			0
$921$		−	1732.93i		−	1.88157i
$922$			349.187i			0.378728i
$923$	691.286			0.748956
$924$	997.752	−	229.263i	1.07982	−	0.248120i
$925$		0			0
$926$			1331.87i			1.43830i
$927$		−	1405.84i		−	1.51655i
$928$		−	951.209i		−	1.02501i
$929$	−298.522			−0.321337			−0.160669	−	0.987008i	$-0.551365\pi$
$929$	−298.522			−0.321337			−0.160669	+	0.987008i	$0.551365\pi$
$930$		0			0
$931$		−	244.138i		−	0.262232i
$932$	−475.716			−0.510425
$933$		−	1424.76i		−	1.52708i
$934$			1175.47i			1.25854i
$935$		0			0
$936$	243.978			0.260661
$937$	−708.598			−0.756241			−0.378120	−	0.925756i	$-0.623429\pi$
$937$	−708.598			−0.756241			−0.378120	+	0.925756i	$0.623429\pi$
$938$		−	617.571i		−	0.658391i
$939$	164.487			0.175173
$940$		0			0
$941$			286.193i			0.304137i	0.988370	+	0.152069i	$0.0485934\pi$
$941$			286.193i			0.304137i	−0.988370	+	0.152069i	$0.951407\pi$
$942$	944.884			1.00306
$943$	209.961			0.222652
$944$	−464.251			−0.491792
$945$		0			0
$946$	468.651	+	2039.57i	0.495403	+	2.15600i
$947$		−	1220.02i		−	1.28829i	−0.764901	−	0.644147i	$-0.777212\pi$
$947$		−	1220.02i		−	1.28829i	0.764901	−	0.644147i	$-0.222788\pi$
$948$	1067.06			1.12559
$949$	−458.284			−0.482913
$950$		0			0
$951$	−552.842			−0.581327
$952$	81.5263			0.0856368
$953$	−1539.71			−1.61564			−0.807821	−	0.589428i	$-0.799353\pi$
$953$	−1539.71			−1.61564			−0.807821	+	0.589428i	$0.799353\pi$
$954$			5688.64i			5.96293i
$955$		0			0
$956$			906.301i			0.948013i
$957$	−293.104	−	1275.59i	−0.306274	−	1.33291i
$958$			439.846i			0.459130i
$959$			208.282i			0.217186i
$960$		0			0
$961$	−338.104			−0.351825
$962$			1331.55i			1.38415i
$963$	858.633			0.891623
$964$		−	441.843i		−	0.458343i
$965$		0			0
$966$	−1375.82			−1.42424
$967$	−1504.21			−1.55555			−0.777773	−	0.628546i	$-0.783651\pi$
$967$	−1504.21			−1.55555			−0.777773	+	0.628546i	$0.783651\pi$
$968$	77.7029	−	37.6994i	0.0802716	−	0.0389457i
$969$	−1193.61			−1.23180
$970$		0			0
$971$	−676.492			−0.696696			−0.348348	−	0.937365i	$-0.613257\pi$
$971$	−676.492			−0.696696			−0.348348	+	0.937365i	$0.613257\pi$
$972$			1700.47i			1.74945i
$973$			509.720i			0.523864i
$974$		−	2339.71i		−	2.40216i
$975$		0			0
$976$			1375.60i			1.40943i
$977$		−	588.072i		−	0.601916i	−0.953637	−	0.300958i	$-0.902694\pi$
$977$		−	588.072i		−	0.601916i	0.953637	−	0.300958i	$-0.0973064\pi$
$978$	2080.53			2.12734
$979$	−363.236	−	1580.81i	−0.371028	−	1.61472i
$980$		0			0
$981$		−	274.393i		−	0.279707i
$982$		−	910.614i		−	0.927306i
$983$		−	824.978i		−	0.839245i	−0.907699	−	0.419622i	$-0.862162\pi$
$983$		−	824.978i		−	0.839245i	0.907699	−	0.419622i	$-0.137838\pi$
$984$	41.7966			0.0424762
$985$		0			0
$986$			1521.17i			1.54277i
$987$	623.116			0.631323
$988$			496.555i			0.502586i
$989$		−	1359.62i		−	1.37475i
$990$		0			0
$991$	−1747.44			−1.76331			−0.881653	−	0.471899i	$-0.843569\pi$
$991$	−1747.44			−1.76331			−0.881653	+	0.471899i	$0.843569\pi$
$992$	−1106.64			−1.11557
$993$			768.902i			0.774323i
$994$	−548.985			−0.552299
$995$		0			0
$996$			980.261i			0.984198i
$997$	−1069.45			−1.07267			−0.536333	−	0.844007i	$-0.680191\pi$
$997$	−1069.45			−1.07267			−0.536333	+	0.844007i	$0.680191\pi$
$998$	−1533.62			−1.53669
$999$	2156.69			2.15885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.d.b.274.14		16
5.2	odd	4		275.3.c.h.76.7	yes	8
5.3	odd	4		275.3.c.g.76.2	✓	8
5.4	even	2	inner	275.3.d.b.274.3		16
11.10	odd	2	inner	275.3.d.b.274.4		16
55.32	even	4		275.3.c.h.76.2	yes	8
55.43	even	4		275.3.c.g.76.7	yes	8
55.54	odd	2	inner	275.3.d.b.274.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.c.g.76.2	✓	8	5.3	odd	4
275.3.c.g.76.7	yes	8	55.43	even	4
275.3.c.h.76.2	yes	8	55.32	even	4
275.3.c.h.76.7	yes	8	5.2	odd	4
275.3.d.b.274.3		16	5.4	even	2	inner
275.3.d.b.274.4		16	11.10	odd	2	inner
275.3.d.b.274.13		16	55.54	odd	2	inner
275.3.d.b.274.14		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.78271 q^{2} +5.54645i q^{3} +3.74350 q^{4} +15.4342i q^{6} -4.48239 q^{7} -0.713764 q^{8} -21.7632 q^{9} +(2.46337 + 10.7206i) q^{11} +20.7632i q^{12} +15.7063 q^{13} -12.4732 q^{14} -16.9602 q^{16} +25.4820 q^{17} -60.5607 q^{18} +8.44528i q^{19} -24.8614i q^{21} +(6.85487 + 29.8324i) q^{22} -19.8870i q^{23} -3.95886i q^{24} +43.7063 q^{26} -70.7903i q^{27} -16.7798 q^{28} +21.4524i q^{29} +24.9579 q^{31} -44.3404 q^{32} +(-59.4615 + 13.6630i) q^{33} +70.9092 q^{34} -81.4704 q^{36} +30.4659i q^{37} +23.5008i q^{38} +87.1145i q^{39} +10.5577i q^{41} -69.1821i q^{42} +68.3676 q^{43} +(9.22164 + 40.1327i) q^{44} -55.3397i q^{46} +25.0636i q^{47} -94.0690i q^{48} -28.9082 q^{49} +141.335i q^{51} +58.7967 q^{52} -93.9329i q^{53} -196.989i q^{54} +3.19936 q^{56} -46.8414 q^{57} +59.6960i q^{58} +27.3730 q^{59} -81.1075i q^{61} +69.4507 q^{62} +97.5509 q^{63} -55.5457 q^{64} +(-165.464 + 38.0202i) q^{66} +49.5118i q^{67} +95.3920 q^{68} +110.302 q^{69} +44.0132 q^{71} +15.5338 q^{72} -29.1783 q^{73} +84.7779i q^{74} +31.6149i q^{76} +(-11.0418 - 48.0540i) q^{77} +242.415i q^{78} -51.3920i q^{79} +196.767 q^{81} +29.3792i q^{82} +47.2115 q^{83} -93.0685i q^{84} +190.248 q^{86} -118.985 q^{87} +(-1.75827 - 7.65199i) q^{88} -147.455 q^{89} -70.4019 q^{91} -74.4468i q^{92} +138.428i q^{93} +69.7449i q^{94} -245.932i q^{96} -87.8176i q^{97} -80.4433 q^{98} +(-53.6108 - 233.315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{4} - 64 q^{9} - 2 q^{11} - 36 q^{14} - 28 q^{16} + 136 q^{26} - 84 q^{31} + 284 q^{34} - 168 q^{36} - 138 q^{44} + 100 q^{49} + 332 q^{56} + 320 q^{59} - 576 q^{64} - 630 q^{66} + 32 q^{69}+ \cdots - 736 q^{99}+O(q^{100}) \) 16 * q + 20 * q^4 - 64 * q^9 - 2 * q^11 - 36 * q^14 - 28 * q^16 + 136 * q^26 - 84 * q^31 + 284 * q^34 - 168 * q^36 - 138 * q^44 + 100 * q^49 + 332 * q^56 + 320 * q^59 - 576 * q^64 - 630 * q^66 + 32 * q^69 + 492 * q^71 + 608 * q^81 - 564 * q^86 + 36 * q^89 - 284 * q^91 - 736 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more